The subject invention relates to the field of medical technology and can provide for an improved method of creating composite images from a plurality of individual signals. The subject invention is particularly advantageous in the field of magnetic resonance imaging (MRI) where many individual images can be used to create a single composite image.
In the early stages of MRI development, typical MRI systems utilized a single receiver channel and radio frequency (RF) coil. In order to improve performance, multi-coil systems employing multiple RF coils and receivers can now be utilized. During operation of these multi-receiver systems, each receiver can be used to produce an individual image of the subject such that if there is n receivers there will be n images. The n images can then be processed to produce a single composite image.
Many current systems incorporate a sum-of-squares (SOS) algorithm, where the value of each pixel in the composite image is the square-root of the sum of the squares of the corresponding values of the pixels from each of the n individual images. Where the pixel values are complex, the value of each pixel in the composite image is the square-root of the sum of the magnitude squared of the corresponding pixels from each of the individual images. In mathematical terms, if n coils produce n signals S=[s1, s2, . . . , sn] corresponding to the pixel values from a given location, the composite signal pixel is given by the following equation:
                    S        *            ·      S        =                              ∑                      j            =            1                    n                ⁢                                                                                        ⁢                              S                j                                      _                    ·                      S            j                                =                            ∑                      j            =            1                    n                ⁢                                        S            j                                        where S* is the conjugate row-column transpose of the column vector, S. Some systems also incorporate measurement and use of the noise variances of each coil. Define the n×n noise covariance matrix, N, in terms of noise expectation <•>, by the formula:Ni,j=(si−<si>)·{overscore ((sj−<sj>))}The diagonal entries of N are the noise variances of each coil. Each of the n individual channel gains can then be adjusted after acquisition to produce equal noise variance individual images. Following this procedure, the SOS algorithm can then be applied. This additional procedure tends to improve the signal-to-noise ratio (SNR) of the process but may still fail to optimize the SNR of the resultant composite image. This results in an equation:√{square root over (S*·[Diag(N)]−1·S)}
It can be shown that the SOS algorithm is optimal if the noise covariance matrix is the identity matrix. In order to further optimize the SNR of the resultant composite image, it would be helpful to have knowledge of the noise covariance matrix. Optimal SNR reconstruction in the presence of noise covariance can be summarized by the following simple equation:√{square root over (S*·[N]−1·S)}U.S. Pat. Nos. 4,885,541 and 4,946,121 discuss algorithms relating to equations which are similar in form. Typically this method is applied in the image domain, after acquisition and Fourier transformation into separate images.